Difference when omitting the C++ template argument list

Question

When can you omit the C++ template argument list? For example in Visual Studio 2010 this piece of code compiles fine:

template<class T>
Vec2<T> Vec2<T>::operator+ (const Vec2 &v) const
{
    return Vec2(x + v.x, y + v.y);
}

If you inline the code, it actually compiles without any argument list. But is this really the same as the following version?

template<class T>
Vec2<T> Vec2<T>::operator+ (const Vec2<T> &v) const
{
    return Vec2<T>(x + v.x, y + v.y);
}

Answer 1

Inside a class you can omit the argument on the class type:

template<typename K>
struct A {
   A<K> foo1; // legal
   A foo2; // also legal and identical to A<K> foo
   A bar(A x) {...} // same as A<K> bar(A<K> x) {...}
};

Outside of a class scope you need the template arguments:

// legal
template<typename K>
A<K> foo(A<K> x) { return A<K>(); }

// illegal!
template<typename K>
A foo(A x) { return A(); }

If you declare a member function outside the class, you need the template list for the return type and for the class:

// legal
template<typename K>
A<K> A<K>::bar(A<K> x) { return A<K>(x); }

// legal
template<typename K>
A<K> A<K>::bar(A x) { return A(x); }

// illegal!
template<typename K>
A A::bar(A<K> x) { return A<K>(x); }